Interpolando cuatro puntos $(x_{0}, f(x_{0}))$, $(x_{0}+h, f(x_{0}+h))$, $(x_{0}+2h, f(x_{0}+2h))$ y $(x_{0}+3h, f(x_{0}+3h))$, mediante un polinomio de Lagrange e integrando
\begin{equation*} I = \frac{3}{8} h \ [f(x_{0}) + 3 f(x_{0}+h) + 3 f(x_{0}+2h) + f(x_{0}+3h)] \end{equation*}Usando la notación acostumbrada
\begin{equation*} I = \frac{3}{8} h \ [f(x_{i}) + 3 f(x_{i+1}) + 3 f(x_{i+2}) + f(x_{i+3})] \end{equation*}
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